Abstract:
In 2009 J.-P. Serre providied an explicit multiplicative bound for orders of
finite subgroups of plane Cremona group of rank 2 over finitely generated
fields over $Q$ and asked a question: is it true that order of finite subgroups
of Cremona groups of arbitrary rank over mentioned fields are bounded and how
the bound can be estimated?
In 2013, Yu. Prokhorov and C. Shramov answered the first part of the question
in more general setup. They proved that group of birational automorphisms of
arbitrary variety of arbitrary dimension over finitely generated fields over $Q$
has bounded finite subgroups. But their bounds were no longer explicit. I will
discuss how we can try to answer the second part of Serre’s question in case
of $Cr_3(Q)$.
Language: English
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